We report a temperature-dependent high-resolution X-ray diffraction investigation of 200nm epitaxial BiFeO3 thin films grown on (001) SrTiO3. We were successful in making epitaxial thin films thermally stable, a key requirement for this study. Our results provide evidence that BiFeO3 undergoes three ghtemperature transitions: an antiferromagnetic transition at 425 C, a first-order - phase transition between 745 C and 780 C and a smoother transition toward the -phase at 860 C. Both the - and - transitions take place 60 C lower than the bulk values whereas the antiferromagnetic transition occurs 55 C higher. This underscores the part played by strain and also emphasizes that BiFeO3 is not a conventional ferroelectric perovskite. Reciprocal space maps reveal the unusual result that the thin films remain monoclinic on crossing the - phase transition. Linear extrapolation of the in-plane lattice parameters to higher temperatures rules out cubic symmetry for the -phase.